SOLUTION: The product of these two numbers is 12. Their difference is 1. What is their sum?

Question 423116: The product of these two numbers is 12. Their difference is 1. What is their sum?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
We could solve this problem the formal way using variables, or logically, using our heads.
Formal way:
Let x = the smaller number
Then the larger number must be x + 1 since their difference is 1.
So we have x(x+1) = 12 -> x^2 + x - 12 = 0
Using the quadratic formula we have
This gives x = 3, -4
So y = 4, -3
Thus the sum of the two numbers is either 7 or -7.
Logical way:
What two numbers have a product of 12 and a difference of 1?
Only 3 and 4 (and their negatives)
The other pairs of numbers which give a product of 12, 6,2 and 12,1 don't have a difference of 1.

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